1. Field of the Invention
This invention relates to a curve generating method and, more particularly, to a method of generating a three-dimensional curve which becomes necessary when generating a curved surface.
2. Description of the Related Art
A curved surface of a three-dimensional metal mold or the like on a design drawing is generally expressed by a plurality of section curves, but no profile data is shown for the shape of the area lying between a certain section curve and the next adjacent section curve. In numerically controlled machining it is essential that machining be carried out so as to smoothly connect these two section curves despite the fact that the profile between them is not given In other words, this means that machining must be performed by generating the curved surface between the two section curves from such data as that indicative of the section curves, recording on an NC tape the data concerning the generated curved surface, and carrying out machining in accordance with commands from the NC tape. To this end, there has been proposed a method of generating the curved surface of a three-dimensional curved body in accordance with predetermined rules using data (e.g. section curves and the like) specifying the three-dimensional curved body
FIGS. 5(a)-(d) for describing a curved surface generating method, in which a curved surface CS [see FIG. 5(c)]is generated by providing three-dimensional curves (reference curves) 11a, 11b [see FIG. 5(a)]of a curved surface cut by a predetermined section, dividing each of the reference curves 11a, 11b into N equal segments [see FIG. 5(b)], and connecting corresponding ones of the partitioning points by straight lines
In this curved surface generating method, the reference curves 11a, 11b, which are the three-dimensional curves, must be specified. To this end, a sequence of discrete points P.sub.li (x.sub.i,y.sub.i,z.sub.i) (i=1,2, . . . ) is given with regard to the reference curve 11a, as shown in FIG. 5(d), a sequence of discrete points P.sub.2j (x.sub.j,y.sub.j,z.sub.j) (j=1,2,...) is given with regard to the reference curve 11b. and curves (reference curves) connecting these point sequences are obtained by performing interpolation between points so as to smoothly connect the respective point sequences.
In this conventional method of generating the point sequence connecting curves, it is necessary to determine a tangent vector at each point However, the method of determining these tangent vectors is a major undertaking requiring matrix computations, inverse matrix computations, etc., and it is impossible for an ordinary curved surface generating apparatus on the personal computer level to determine the tangent vectors.